Practice Set 1.1
Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 . (i)…
3a + 5b = 26; a + 5b = 22 Solve the following simultaneous equation.…
x + 7y = 10; 3x - 2y = 7 Solve the following simultaneous equation.…
2x - 3y = 9; 2x + y = 13 Solve the following simultaneous equation.…
5m - 3n = 19; m - 6n = -7 Solve the following simultaneous equation.…
5x + 2y = -3; x + 5y = 4 Solve the following simultaneous equation.…
1/3 x+y = 10/3 2x + 1/4 y = 11/4 Solve the following simultaneous equation.…
99x + 101 y = 499; 101x + 99y = 501 Solve the following simultaneous equation.…
49x - 57y = 172; 57x - 49y = 252 Solve the following simultaneous equation.…
Practice Set 1.1
Question 1.Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 ……. (i)
2x + 3y = 12 ……… (ii)
Answer:
5x + 3y = 9 ……. (i)
2x + 3y = 12 ……… (ii)
Subtracting equation (ii) from (i), we get,(5x + 3y ) - (2x + 3y) = 9 - 12
5x - 2x + 3y - 3y = -3
3x = -3
x = -1
Putting the value of x in equation (i),
5(-1) + 3y = 9
-5 + 3y = 9
3y = 14
y = 14/3
Let’s add equations (I) and (II).
Hence, x = -1 and y = 14/3 is the solution of the equation.
Question 2.
Solve the following simultaneous equation.
3a + 5b = 26; a + 5b = 22
Answer:
Change the sign of Eq. (II)
Substituting a = 2 in Eq. (II)
∴ solution is (a, b) = (2, 4)
Question 3.
Solve the following simultaneous equation.
x + 7y = 10; 3x – 2y = 7
Answer:
Multiply Eq. I by 2 and Eq. II by 7
x=3
Substituting x= 3 in Eq. I
7y=7
y=1
∴ Solution is (x , y) = (3, 1)
Question 4.
Solve the following simultaneous equation.
2x – 3y = 9; 2x + y = 13
Answer:
Change the sign of Eq. (II)
Substituting y = 1 in Eq. (II)
2x = 13 - 1
2x = 12
x = 6
∴ solution is (x, y) = (1,6)
Question 5.
Solve the following simultaneous equation.
5m – 3n = 19; m – 6n = –7
Answer:
Multiply Eq. II by 5
equating (I) and (III), change the sign of Eq. (III)
⇒ 
⇒ 
⇒ n = 2
Substituting n = 2 in Eq 1
⇒ 5m - 3(2) = 19
⇒ 5m - 6 = 19
⇒ 5m = 25
⇒ m = 5
∴ Solution is (m , n) = (5, 2)
Question 6.
Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4
Answer:
Multiply Eq. I by 5 and Eq. II by 2
Change sign of Eq.(IV)
Subsituting x=–1in Eq.II
∴ solution is (x, y) = (–1, 1)
Question 7.
Solve the following simultaneous equation.
Answer:
⇒ 
⇒ 
⇒ 
⇒ 
Multiplying Eq. II by 3
Equating Eq. I and III, change the signs of Eq. III
Substituting x = 1 in Eq. I
∴ solution is (x,y) = (1, 3)
Question 8.
Solve the following simultaneous equation.
99x + 101 y = 499; 101x + 99y = 501
Answer:
Adding both the Equations
Dividing both sides by 200
…(III)
Subtract equation (I) and (II)
Divide both sides by (–2)
…(IV)
Equating Eq. (III) and (IV)
Substituting x=3 in Eq. III
∴ solution is (x, y) = (3, 2)
Question 9.
Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252
Answer:
Adding both the Equations
Dividing both sides by 106
…(III)
Subtract equation (I) and (II)
Divide both sides by (–8)
…(IV)
Equating Eq. (III) and (IV)
Substituting x=7 in Eq. IV
∴ solution is (x, y) = (7,3)
